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X(2), X(4), X(69), X(459), X(1440), X(6616), X(7080), X(37669), X(64986), X(66090), X(66091)

vertices of the cevian triangles of X(69) and X(37669)

extraversions of the weak points X(1440), X(7080)

Let ABC be a triangle, P a point and A'B'C' the circumcevian triangle of P. Let A", B", C" be the orthogonal projections of A', B', C' on BC, CA , AB respectively. The locus of P such that AA", BB", CC" are concurrent (at Q) is K004 (A. Boutin, Journal de mathématiques élémentaires, 1892, pp.156 - 157). The locus of Q is Q189.

See the very similar Q172, the Darboux (first) sextic.

Q189 is a self-isotomic circum-sextic with double points A, B, C whose nodal tangents are the cevian lines of X(4) and X(459).

G is a quadruple point with tangents passing through X(7) and extraversions.

If P1, P2 are two isogonal conjugates on K004, then the corresponding points Q1, Q2 are two isotomic conjugates on Q189.